Abstract
We show that Poisson integrals belonging to certain weighted harmonic Bergman spaces b δ p on the upper half-space must have the moment vanishing properties. As an application, we show that b 0 p , p⩾1, contains a dense subspace whose members have the horizontal moment vanishing properties. Also, we derive related weighted norm inequalities for Poisson integrals. As a consequence, we obtain a characterization for Poisson integrals of continuous functions with compact support in order to belong to b δ p .
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